CAIE A-Level Mathematics AS 1.5.1 Trig Graphs Questions

Practise sketching sine, cosine and tangent graphs in degrees or radians and reading amplitude, period, range, intercepts, extrema and solution counts after transformations.

Exam points

Sketch sine, cosine or tangent graphs over a stated domain, including changes to amplitude, period, phase or vertical position.
Read a trigonometric graph or its equation to determine parameters, intercepts, extrema, range or coordinates of specified points.

[Maximum number: 3]

Figure for Question CAIE A-Level Mathematics AS 1.5.1 Trig Graphs Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve $y=k \cos \left(x-\frac{1}{6} \pi\right)$ where k is a positive constant and x is measured in radians. The curve crosses the x-axis at point A and B is a minimum point.

Find the coordinates of A and B.

State $\left(\frac{5}{3} \pi, 0\right)$ for point A
Or exact equivalent.

Marking guidance:

Allow $x=\frac{5}{3} \pi$ or exact equivalent.

$x=\frac{19}{6} \pi$ for point B
Or exact equivalent.
May be implied in coordinate or vector form.

y=-k for point B
May be implied in coordinate or vector form.

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CAIE A-Level Mathematics AS 1.5.1 Trig Graphs Questions question 1